integral of (x^2-15)/(x+7)

Lösung

\int \frac{x ^{2} - 15}{x + 7} d x

\frac{1}{2} (x + 7)^{2} - 14 x - 98 + 34 ln ∣ x + 7 ∣ + C

Schritte zur Lösung

\int \frac{x ^{2} - 15}{x + 7} d x

Multipliziere aus

\frac{x ^{2} - 15}{x + 7} : \frac{x ^{2}}{x + 7} - \frac{15}{x + 7}

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{x ^{2}}{x + 7} d x - \int \frac{15}{x + 7} d x

\int \frac{x ^{2}}{x + 7} d x = \frac{( x + 7 ) ^{2}}{2} - 14 (x + 7) + 49 ln ∣ x + 7 ∣

\int \frac{15}{x + 7} d x = 15 ln ∣ x + 7 ∣

= \frac{( x + 7 ) ^{2}}{2} - 14 (x + 7) + 49 ln ∣ x + 7 ∣ - 15 ln ∣ x + 7 ∣

Vereinfache

\frac{( x + 7 ) ^{2}}{2} - 14 (x + 7) + 49 ln ∣ x + 7 ∣ - 15 ln ∣ x + 7 ∣ : \frac{1}{2} (x + 7)^{2} - 14 x - 98 + 34 ln ∣ x + 7 ∣

= \frac{1}{2} (x + 7)^{2} - 14 x - 98 + 34 ln ∣ x + 7 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (x + 7)^{2} - 14 x - 98 + 34 ln ∣ x + 7 ∣ + C

y^{^{''}} - 2 y^{^{'}} = 9 x

\int_{0}^{2} (3 x^{2} - 2) d x

d er i v a t i v e (2 + u^{2})^{5} (5 - 9 u^{2})^{8}

t an g e n t f (x) = 5 + 4 x^{2} - 2 x^{3}, (1, 7)

\int \frac{( 3 x ^{2} - 4 ) ^{\frac{3}{2}} 4 x ^{3}}{x ^{2}} d x